The present invention relates in general to systems, methods, and algorithms for describing and implementing networks with parallel and series elements. More particularly, the invention relates to the systematic design and implementation of networks using combinations of matching series and parallel elements.
In a network (M) which may be characterized by the quotient of a cross-quantity and a through-quantity, M=cross-quantity/through-quantity, it is generally known that certain relationships govern series and parallel network elements. For example, in an electrical resistor network, resistance (R) is the quotient of voltage (V) and current (i), R=V/i. It is well known that series elements are additive, e.g. Requivalent=(R1+R2+R3+. . . RN), and that the equivalent resistance of parallel resistor elements is described by the relationship, Requivalentxe2x88x921=(R1xe2x88x921+R2xe2x88x921+R3xe2x88x921+. . . RNxe2x88x921). Such relationships hold true for other physical networks M as well.
In many engineering applications the problem of how to implement a network using multiple identical elements is encountered. Often such an implementation is sought in order to reduce the influence of unfavorable factors. In integrated circuit layout for example, the effects of an uneven temperature gradient, nonuniform distribution of process layers, and noise emissions from adjacent circuit blocks, may be alleviated by implementing a desired network value, such as resistance or capacitance, using smaller individual elements rather than using one lump-sum component.
Problems arise however, in attempting to describe a network using a combination of series and parallel elements. It is often desirable to use elements with matching physical characteristics. The use of matching network elements helps to equalize the effects of thermal gradients and material gradients and other unfavorable factors. The use of matching elements is also often desirable from a manufacturing standpoint. It is known in the arts to approach the breakdown of a network into series and parallel elements using some degree of trial and error. The problem is made more complex by concerns such as, in the example of integrated circuit and design, the desire to minimize die area and the desire to minimize the count of individual network elements or to utilize elements of a particular value or size.
It would be useful and advantageous in the arts to provide algorithms, systems, and methods for systematically describing networks in terms of series and parallel elements. Additional uses and advantages would be inherent in algorithms, systems, and methods also capable of optimizing a network implementation while reducing the need for manual trial and error approaches common in the arts.
In general, the present invention provides systems, methods, and algorithms for designing and implementing networks using a combination of series and parallel elements.
According to a preferred embodiment of the invention, an algorithm for determining the physical implementation of a network with a combination of matching series and parallel elements defines the network in terms of a network value representing the assembled value of the total equivalence of the elements. The network value is divided into an integer part and a proper fraction part. A partial quotient and residue are computed for the proper fraction part. Additional partial quotients and residues may be computed while the residue remains significant. The physical implementation of the network is then described in terms of series and parallel elements represented by the integer part and the partial quotients.
According to another aspect of the invention, a significance level for the residue is selected.
According to still another aspect of the invention, alternative expressions may be used for the division of the network value into an integer part and a proper fraction part.
According to yet another aspect of the invention, a physical implementation of the network is selected based on one or more optimization criteria.
According to one preferred embodiment of the invention, a method of assembling a network from a combination of series and parallel elements is provided. A network value consisting of an integer part and a proper fraction part is used to represent the network. A partial quotient and residue are computed for the proper fraction part, using as many iterations as needed until the residue becomes insignificant. The physical implementation of the network is described in terms of series and parallel elements represented by the integer part and the partial quotients. The described series and parallel elements are coupled to assemble the network.
According to another aspect of the invention, the network may be optimized by selecting the minimum number of elements.
According to another aspect of the invention, the network may be optimized by selecting the minimum value of an object function of the elements such as the total area occupied by the elements.
According to another aspect of the invention, a step of selecting a matching tolerance for the series and parallel elements may be used.
According to another aspect of the invention, an element value may be preselected for use in determining network implementations using a quantity of the preselected-value elements deployed in series and in parallel.
According to another embodiment of the invention, a system for constructing a network from a combination of matching series and parallel elements is provided. The system includes means for executing an algorithm to determine the physical implementation of the network and means for coupling a quantity of matching series and parallel elements to form the network.
The invention provides several technical advantages including but not limited to increased efficiency in network design and implementation, improved accuracy in network design and network component matching, and efficiency in providing design alternatives for use in evaluating potential network layouts according to selected optimization criteria.